Problem: Right now you are to solve a very, very simple problem — to crack the safe. Four positive integers stand one by one on a circle protecting the safe. You know that to unlock this striking safe you have to make all four numbers equal to one. Operations are as follows: you may choose two adjacent numbers and increase both by one; you may choose two adjacent even numbers and divide both by two. Nothing else. Crack the safe!

Input

The single line of the input contains four space-separated integer positive numbers not greater than 109 each — four numbers on the circle in consecutive order.

Output

The output should contain "-1" (quotes for clarity) if the safe is secure, that is it's impossible to crack it. Otherwise, output should contain the sequence of operations (one operations per line) leading to unlocking the safe. You don't have to minimize the number of operations, but it should not exceed 1000. To make things clear, assume numbers stand on positions 1 through 4. Each operation is encoded by two symbols. If the following operation is dividing then first symbol is '/'; otherwise it's '+' (addition). The second symbol is the position of the first number in pair in consecutive order. (see samples for clarification).

If there are several solutions, output any of them.

Examples

Input

1 1 1 1


Output



Input

1 2 4 2


Output

/2
/3


Input

3 3 1 1


Output

+1
/1
/1


Input

2 1 2 4


Output

/3
/4

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Locale;
import java.util.StringTokenizer;
import java.util.TreeSet;

@SuppressWarnings("unchecked")
public class C implements Runnable {
        static int[][] queue = new int[4][2000000];

        static long mul;

        static long getString(int v) {
                long hkey = 0l;
                for (int i = 0; i < 4; ++i) {
                        hkey = hkey * mul + queue[i][v];
                }
                return hkey;
        }

        class State implements Comparable<State> {
                int pos;
                int dist;
                long sum;
                int shift = 0;
                String s;
                State prev;
                int c;

                public State(int pos, int dist, String s, State prev, int shift) {
                        this.pos = pos;
                        this.dist = dist;
                        this.s = s;
                        this.prev = prev;
                        this.shift = shift % 4;
                        sum = 0;
                        c = 0;
                        for (int i = 0; i < 4; ++i) {
                                sum += queue[i][pos];
                                c += (queue[i][pos] % 2 == 0 && queue[(i + 1) & 3][pos] % 2 == 0) ? 1 : 0;
                        }
                }

                public int compareTo(State that) {
//                      for (int i = 0; i < 4; ++i) {
//                              int diff = queue[i][pos] - queue[i][that.pos];
//                              if (diff != 0) {
//                                      return diff;
//                              }
//                      }
                        if (this.sum != that.sum) {
                        	return Long.signum(this.sum - that.sum);
                        }
                      if (this.c != that.c) {
                              return (that.c - this.c);
                      }
                      if (this.dist != that.dist) {
                    	  return this.dist - that.dist;
                      }
                        return pos - that.pos;
                }
        }

        private void solve() throws Exception {

                for (long l = (long) 1e17;; --l) {
                        if (BigInteger.valueOf(l).isProbablePrime(50)) {
                                mul = l;
                                break;
                        }
                }
                // System.err.println(mul);
                HashSet<Long> map = new HashSet<Long>();
                TreeSet<State> states = new TreeSet<State>();

                int ql = 0;
                int qr = 0;
                long sum = 0;
                for (int i = 0; i < 4; ++i) {
                        queue[i][0] = nextInt();
                        sum += queue[i][0];
                }
                if (sum == 4) {
                        println("");
                        return;
                }
                states.add(new State(0, 0, "", null, 0));
                map.add(getString(0));
                qr++;

                int[] a = new int[4];
                int[] aa = new int[4];
                int[] bb = new int[4];
                boolean[] canDiv = new boolean[4];
                while (!states.isEmpty()) {
                        State state = states.first();
                        states.remove(state);
                        ql = state.pos;
                        long tsum = 0;
                        for (int i = 0; i < 4; ++i) {
                                a[i] = queue[i][ql];
                                tsum += a[i];
                        }
                        if (tsum > sum + 20) {
                                continue;
                        }
                        int shift = state.shift;
                        boolean can = false;
                        for (int i = 0; i < 4; ++i) {
                                if ((a[i] & 1) == 0 && (a[(i + 1) & 3] & 1) == 0) {
                                        can = true;
                                        boolean allOne = true;
                                        for (int j = 0; j < 4; ++j) {
                                                bb[j] = (j == i || j == (((i + 1) & 3))) ? (a[j] >> 1)
                                                                : a[j];
                                                allOne &= bb[j] == 1;
                                        }
                                        int min = 0;
//                                      j: for (int j = 1; j < 4; ++j) {
//                                              for (int k = 0; k < 4; ++k) {
//                                                      int diff = bb[(j + k) & 3]
//                                                                      - bb[(min + k) & 3];
//                                                      if (diff > 0) {
//                                                              continue j;
//                                                      }
//                                                      if (diff < 0) {
//                                                              min = j;
//                                                              continue j;
//                                                      }
//                                              }
//                                      }
                                        for (int j = 0; j < 4; ++j) {
                                                aa[j] = bb[(j + min) & 3];
                                        }
                                        for (int j = 0; j < 4; ++j) {
                                                queue[j][qr] = aa[j];
                                        }

                                        long s = getString(qr);
                                        if (!map.contains(s)) {
                                                final String t = "/" + ((shift + i) % 4 + 1);
                                                map.add(s);
                                                states.add(new State(qr, state.dist + 1, t, state,
                                                                shift + min));
                                                qr++;
                                                if (allOne) {
                                                        ArrayList<String> ans = new ArrayList<String>();
                                                        ans.add(t);
                                                        while (state.prev != null) {
                                                                ans.add(state.s);
                                                                state = state.prev;
                                                        }
                                                        Collections.reverse(ans);
                                                        for (String ss : ans) {
                                                                println(ss);
                                                        }
                                                        return;
                                                }
                                        }
                                }
                        }
//                      if (can) {
//                              continue;
//                      }
                        for (int i = 0; i < 4; ++i) {
                                for (int j = 0; j < 4; ++j) {
                                        if ((j == i || j == (((i + 1) & 3)))) {
                                                bb[j] = a[j] + 1;
                                        } else {
                                                bb[j] = a[j];
                                        }
                                }
                                for (int j = 0; j < 4; ++j) {
                                        canDiv[j] = (bb[j] & 1) == 0;
                                }
                                if (!(canDiv[i] && canDiv[(i + 1) & 3] || canDiv[(i + 1) & 3]
                                                && canDiv[(i + 2) & 3])) {
                                        continue;
                                }
                                int min = 0;
//                              j: for (int j = 1; j < 4; ++j) {
//                                      for (int k = 0; k < 4; ++k) {
//                                              int diff = bb[(j + k) & 3]
//                                                              - bb[(min + k) & 3];
//                                              if (diff > 0) {
//                                                      continue j;
//                                              }
//                                              if (diff < 0) {
//                                                      min = j;
//                                                      continue j;
//                                              }
//                                      }
//                              }
                                for (int j = 0; j < 4; ++j) {
                                        aa[j] = bb[(j + min) & 3];
                                }
                                for (int j = 0; j < 4; ++j) {
                                        queue[j][qr] = aa[j];
                                }
                                long s = getString(qr);
                                if (!map.contains(s)) {
                                        final String t = "+" + (i + 1);
                                        map.add(s);
                                        states.add(new State(qr, state.dist + 1, t, state, shift
                                                        + min));
                                        qr++;
                                }
                        }
                }
                throw new AssertionError();
        }

        private BufferedReader reader;
        private PrintWriter writer;
        private StringTokenizer tokenizer;

        public void run() {
                try {
                        reader = new BufferedReader(new InputStreamReader(System.in));
//                      reader = new BufferedReader(new FileReader("a.in"));
                        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
                                        System.out)));

                        solve();

                        reader.close();
                        writer.close();
                } catch (Throwable e) {
                        throw new AssertionError(e);
                }
        }

        private void print(final Object o) {
                writer.print(o);
        }

        private void println(final Object o) {
                writer.println(o);
        }

        private void printf(final String format, final Object... o) {
                writer.printf(format, o);
        }

        private double nextDouble() throws IOException {
                return Double.parseDouble(nextToken());
        }

        private int nextInt() throws IOException {
                return Integer.parseInt(nextToken());
        }

        private long nextLong() throws IOException {
                return Long.parseLong(nextToken());
        }

        private String nextToken() throws IOException {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                        tokenizer = new StringTokenizer(reader.readLine());
                }
                return tokenizer.nextToken();
        }

        public static void main(String[] args) throws InterruptedException {
                final long startTime = System.currentTimeMillis();
                Locale.setDefault(Locale.US);
                final Thread thread = new Thread(null, new C(), "", 1 << 23);
                thread.start();
                thread.join();
//              System.err.printf("%.3f\n",
//                              (System.currentTimeMillis() - startTime) * 0.001);
        }
}